Gear Dynamic Model Research Articles

Dynamic Modeling and Analysis of Epoxy Gear Considering Material Viscoelasticity

With improvements in lubrication and material strength, the power transmitted by plastic gears has increased significantly. To develop high-performance transmission systems, it is necessary to gain deep insights into the dynamic characteristics of plastic gears. However, because plastics are viscoelastic materials, they do not obey Hooke’s law, which is the basis of traditional gear dynamic models. In this study, a refined dynamic model for an epoxy gear pair considering material viscoelasticity and extended tooth contact is established, and the differences in the dynamic responses between an epoxy and a steel gear pair are compared with respect to the dynamic meshing force and dynamic transmission error. The results show that: (1) the plastic gear can restrain the meshing impact, it has a generally lower dynamic meshing force than steel gear pair; (2) the position accuracy is the weak point of plastic gears, and this is significantly affected by the rotation speed; (3) the way to indirectly evaluate the dynamic meshing force by measuring the dynamic transmission error, which is often used for metal gears and is less effective for plastic gears.

Crack detection of powder metal and steel gears

The application of the Powder Metallurgy (PM) method is confirmed as a production technology for gears and other mechanical parts. The PM method offers lightweight, repeatability with high precision, maximum material use, freedom of design, cost efficiency, and sustainability. Condition Monitoring (CM) is an important strategy to adopt in different gear systems. The current paper studies the possibility of crack detection for steel and PM gears to investigate the effect of having different gear materials on fault detection possibility. Four different statistical indicators, namely the RMS, kurtosis, peak value and crest factor are studied. The study is based on calculating Tooth Varying Mesh Stiffness (TVMS) using a calculation model and generating the system dynamic response using a gear dynamic model. Different fault detection indicators are applied to examine the detection possibility with crack propagation. The paper concludes on how having different gear materials has an impact on the fault detection possibility.

Wear prediction considering dynamic load for spur gear in mixed elastohydrodynamic lubrication

In this work, a wear prediction model considering the dynamic load is proposed for spur gears in mixed elastohydrodynamic lubrication (EHL). The dynamic load is calculated by gear dynamic model. Combining gear wear model and dynamic model, the wear depth under the dynamic load is determined and compared with that under quasi-static load. The comparative results show that the maximum wear depth under dynamic load is significantly larger than that under quasi-static load near engaging-in point. The effects of fractional film defect coefficient on wear depth are considerable under dynamic load, which is closely related to gear contact temperature. Furthermore, the effects of surface roughness and gear geometrical parameters on wear depth are studied. The investigation reveals that the wear depth decreases with the increased tooth width, module and pressure angle, but increases with the surface roughness. It illustrates that gear wear depth under the dynamic load can be reduced by optimizing gear geometrical parameters.

Dynamic modeling and vibration analysis of spur gear system considering thin-walled gear and hollow shaft

This paper proposes a gear dynamic model considering the thin-walled gear and hollow shaft. The shell element is adopted to establish the gear-shaft finite element model instead of using the beam element and lumped mass element. The shortcomings of the traditional dynamic model and the influences of thin-walled hollow shafts are analyzed. Numerical results show that the simplification strategy of the traditional dynamic model will lose several vital modal information and evaluate excessive critical speeds. The proposed model obtains the extra resonant frequency in the high-speed region. However, the traditional model loses this phenomenon due to the simplified thin-walled structural features. The equivalence of the hollow shaft to a beam model requires the condition of a small radius-thickness ratio. Otherwise, it will lead to deviations in the predicted vibration characteristics. The proposed model helps to provide a theoretical basis for high-performance design and vibration and noise reduction of high-speed and lightweight gear transmission systems.

Dynamic Analysis of Gear Rattling of a Certain Type of Dual-Clutch Transmission

In order to accurately explore the transmission rattling phenomenon and the influence of different factors on the dynamic characteristics of the gear rattling of the dual-clutch transmission under the condition of preselected gears, this paper establishes the gear rattling dynamics model of the transmission with the 1st gear without preselection and the preselected 4th gear, respectively; The model takes into account factors such as time-varying mesh stiffness, mesh damping, nonlinear oil film force, nonlinear backlash, and the drag torque generated by the clutch in the unengaged state. In addition, the feasibility of the dynamic model was verified by the bench test. On this basis, we took the gear meshing power and system power loss as quantitative indexes to analyze the influence of the preselected gear state and different parameters on the rattle vibration of the transmission. The results show that the pre-selected gear will not have a significant effect on the gears that have been rattled in the non-pre-selected state, and the torque fluctuation of the non-power flow shaft is aggravated by the influence of the transmission power flow branch and transmission ratio at different levels, which makes the overall rattling strength increase. In order to improve the transmission efficiency of the gear, the torque fluctuation of the input end of the system should be reduced as much as possible, and a larger lubricant viscosity can be appropriately selected, the inertia of the empty gear can be properly reduced, and the tooth clearance can be relaxed for selection.

Effects of gear flexibility on the dynamic characteristics of spur and helical gear system

The gear foundation is commonly assumed to be a rigid body in analyzing the dynamic characteristics of the gear system. This modeling approach may not be appropriate for building the gear model with lightweight features. Therefore, this paper proposes a gear dynamic model considering the flexible gear. The shell element with gyroscopic effect is employed to establish the gear finite element model, retaining the gear foundation and teeth structure. The fixed interface modal synthesis method is used to improve computational efficiency. The proposed model is verified by comparing it with the results calculated by Ansys. Based on the proposed model, the effects of gear flexibility on the dynamic characteristics of the spur and helical gear system are investigated. Numerical results show that the developed model can degenerate into the classical gear dynamic model. Due to the assumption of the gear as rigid discs, the predicted resonance speed by the conventional gear dynamic model is larger than the proposed model. Gear flexibility affects the dynamic characteristics of the spur and helical gear system differently. It's worth noting that the dynamic axial meshing force can excite the nodal diameter vibration in the helical gear system. The proposed model provides the theoretical basis and optimization tools for the high-performance design and vibration and noise reduction of high-speed lightweight gear transmission systems.

On the extended tooth contact and nonlinear dynamics for spur gears—An analytical model

In gear mesh, the extended tooth contact is a natural reaction stemming from the elasticity of solid bodies, which inevitably forces the theoretically separated teeth to engage and increases the actual contact ratio. Consequently, the changed mesh stiffness waveforms will further influence the dynamic response. A lot of works are devoted to mesh stiffness representation and dynamic modeling. However, the correlation between extended tooth contact and nonlinear dynamics still needs in-depth study. Motivated by a deeper understanding of the mesh mechanisms and dynamics, this paper proposed an analytical model attempting to combine the extended tooth contact and gear nonlinear dynamics. Starting from the gear elasticity, an analytical mesh stiffness model is proposed, which extended the application ranges of the popular fillet foundation polynomial formulas and covered both thin-walled and thick-walled gears. Moreover, A load-sharing model is developed, which explicitly represented the correlation between torques and intervals of extended tooth contact. Subsequently, the gear torsional dynamic model is extended to embody the extended tooth contact. A series of comparisons with FEM, existing theoretical models, and experiments demonstrated the acceptable accuracy of the present model.

Nonlinear characteristics of gear pair considering fractal surface dynamic contact as internal excitation

A novel gear fractal backlash model is established to better consider joint action of all microscopic asperities on gear dynamics, which has the dynamic form from gear center motion simultaneously in this paper. Based on the fractal surface dynamic contact as internal excitation, a gear dynamic model involving surface morphology and gear center motion is established, and a corresponding close-loop algorithm is proposed to solve system dynamics by combining mesh stiffness and time-varying pressure angle. Accordingly, the chaos of the gear system is analyzed by the bifurcation diagram, phase portraits, and Poincare mapping. The comprehensive and strong influence of dynamic fractal backlash on the nonlinear characteristics of the gear system is also demonstrated. The intense effects of tooth surface topography through fractal backlash are explained in detail. Comparison with experimental data is conducted to verify the superiority of the proposed model.

Investigation of Spur Gear Dynamics with Gear MeshImpacts Induced by Tooth Wear

Abstract Tooth wear is one of the most common faults in gear transmission systems. However, due to its limited influences on gear dynamics, the condition monitoring of gear wear experiences more challenges. To investigate the relationship between tooth wear and gear dynamics, this study develops an eight-degree of freedom dynamic model which takes into account the gear mesh impact induced by tooth wear. In this model, the gear mesh impact force induced by tooth wear was calculated as an extra input excitation for the gear dynamic model. Besides, a comparative study was carried out to explore the real reason that causes the poor dynamic behaviour due to the wear from two points of view: 1) the reduction in gear mesh stiffness; 2) the increase in gear mesh impact force. The simulation results show that the wear causes a slight reduction in gear mesh stiffness, thus leading to the decrease in the amplitude of gear mesh frequency. This is not consistent with the phenomena observed in the lab experiment which shows the increase in the gear vibrations. The second simulation of impact force demonstrates that the wear causes an increase in the impact force which further leads to the increase in the amplitude of gear mesh frequency. This study investigates the cause for the deterioration in gear dynamics induced by gear wear, which can benefit the early condition monitoring and fault diagnosis of the gear tooth wear.

Nonlinear dynamic modeling and analysis of spur gear based on gear compatibility conditions

In the traditional gear dynamic model, the mesh stiffness is obtained under static load. When the mesh stiffness changes greatly with the change of load, the traditional dynamic model is not accurate enough to analyze the gear system. Therefore, this paper proposes a new dynamic model with a more realistic dynamic mesh force based on gear compatibility conditions. The proposed dynamic mesh force model is applicable to the gear system with and without tooth modification and verified by the finite element method. Afterward, the paper compares the differences in the dynamic responses between the proposed model and the traditional model. The results indicate the dynamic responses of the proposed model are generally consistent with those of the traditional model for the standard involute gear system. For the lead crown gear system, compared with the proposed model, the traditional model will lose important nonlinear characteristics in the high-speed area. At most speeds, the amplitudes of vibration and dynamic mesh force of the proposed model are greater than that of the traditional model, especially in the bifurcation, quasi-periodic and chaotic regions.

A Calculation Method for Tooth Wear Depth Based on the Finite Element Method That Considers the Dynamic Mesh Force

Gear wear is a progressive material removal process that gradually changes the tooth profile shape and dynamic mesh force, where the dynamic mesh force affects the tooth surface wear. To describe this process, a spur gear dynamic model that includes the mesh stiffness and unloaded static transmission error (STE) of the worn tooth profile is proposed for calculating the dynamic mesh force. Then, based on the finite element method (FEM), a dynamic contact analysis model that considers the dynamic mesh force is proposed for calculating the time-varying contact stress and relative sliding distance of the tooth surface mesh point. Finally, combined with the Archard wear model, a tooth wear depth calculation method that considers the worn tooth profile and the dynamic mesh force is proposed. In addition, the wear depth and dynamic characteristics under different wear times are studied.

Study on the mesh stiffness and nonlinear dynamics accounting for centrifugal effect of high-speed spur gears

The centrifugal effect is one of the most common phenomena in rotor dynamic systems, while typically ignored in the mesh stiffness evaluation by many research papers. Focusing on the centrifugal force in high-speed working condition, this paper developed an analytical-FEM framework to integrate the centrifugal field into the mesh stiffness and nonlinear dynamics. The additional potential caused by centrifugal force is condensed in the mesh stiffness calculation. The gear torsional dynamic model is further extended to embody the internal dynamic effect in centrifugal field. Solutions of gear statics and dynamics are compared with existing models and experiments, and results demonstrate the reasonable accuracy of the present model.

Dynamic modelling of the gear system under non-stationary conditions using the iterative convergence of the tooth mesh stiffness

This paper presents a new gear dynamic model for the transmission system under the non-stationary condition with the consideration of the coupling between the external load and the internal gear excitation. The gear mesh stiffness variation is found to be the main internal excitation and therefore, the effect of the varying external load on the gear mesh stiffness is evaluated firstly, which can then be incorporated into the gear dynamic model. When the gearbox is subjected to a wide range of external load, the mesh stiffness varies correspondingly and an iterative process is proposed to ensure the convergence of the gear dynamic simulation at each step. The dynamic responses from the model with and without the iterative process have been compared. It indicates that the proposed model can successfully incorporate the external-internal coupling effect in gearbox and further shows that the operating condition has a significant influence on the gear response. The proposed model can provide an effective tool to improve the accuracy of gear dynamic modelling and improve the accuracy of gear fault diagnostics under non-stationary conditions.

Study on vibration characteristics of hydraulic planetary transmission considering engine and torque converter excitation

Large-size vehicle loaders are mainly used in various construction projects with complex working environment, which has a serious impact on the internal vibration of the whole system. In this study, the vibration characteristics of hydraulic planetary transmission of vehicle loader considering the influence of the external excitation are evaluated theoretically and experimentally. The output torque of the four-stroke six-cylinder diesel engine is obtained by force calculation of crank and connecting rod mechanism. The equivalent stiffness and damping of the torque converter are solved according to the torsional dynamic equation of the torque converter. The trapped oil area, oil pressure, and flow rate of gear meshing part are extracted to obtain the trapped oil pressure of variable-speed pump. Then, the multi-degree-of-freedom gear system dynamic model is established to calculate the meshing force, which is applied to vibration response analysis model by using mode superposition method. Lastly, the vibration response test is performed on the experimental prototype to verify the calculation method. The conclusion shows that the generation principle of external excitation and its calculation method in this paper are feasible in the analysis of dynamic characteristics of hydraulic planetary torque converter.

Numerical and experimental study of gear rattle based on a refined dynamic model

A refined single pair gear dynamic model is established to accurately predict the gear rattle. The model considers various key parameters, such as backlash, time-varying mesh stiffness, nonlinear oil film force between teeth and drag torque. The time-varying mesh stiffness of helical gears is calculated by using the potential energy method. The nonlinear oil film force is introduced into the model by considering the entrainment and squeeze effects of the lubricating oil between the teeth. In addition, the friction resistance caused by the squeeze of lubricating oil between the teeth is considered in the proposed model. The rotation speed and angular acceleration of the loose gear were measured on the bench, and compared with the simulation results, which proved the accuracy of the model. The results of the parametric analysis show that excessive torque fluctuation and backlash may lead to severe impact of the gear pair. Increasing the drag torque has a positive effect on the control of the gear rattle. Larger viscosity will make faster attenuation of high frequency impact and reduce the impact strength.

Vibration feature of spur gear transmission with non-uniform depth distribution of tooth root crack along tooth width

Gear tooth root crack is a typical fault of gear transmissions and it threatens the operation safety of gear systems. Therefore, precise detection of the tooth root crack is of a great significance for the prevention of serious safety accidents. As one of the commonly used methods, vibration-based detection has drawn great attentions. However, the mapping relationship between the vibrations and the severity of tooth root crack has not been established well, especially for the crack with non-uniform distribution due to the complexity of its dynamic modelling. To address this problem, an improved gear dynamics model considering non-uniform distribution of the gear tooth root crack fault is established in this paper by using the ‘slice method’. Compared with the traditional methods, the advantage of the proposed model is that it enables the accurate modelling of the non-uniform dynamic mesh forces along tooth width that will further excite the support bearings. Then, the dynamic simulation of the gear transmission with non-uniform tooth root crack is performed. The results indicate that the improved model can reveal the vibration characteristics of the gear transmission due to the extra roll and yaw motions caused by the non-uniform tooth root crack. In addition, the correlation between the vibration and the crack size and location is quantified. This study could provide theoretical reference for quantitative detection and diagnosis of gear tooth root crack.

A novel estimation method of friction coefficient for evaluating gear pitting fault

In present, the model-based gear dynamics is the main method for gear pitting fault diagnosis. However, most of gear dynamic models use a constant friction coefficient or friction coefficient obtained by calculation method that contains many simplifications and assumptions. Especially when a gear has fault, previous studies lack calculation of friction coefficient. In this paper, a new method is proposed to estimate the friction coefficient of gear pairs with different pitting. Based on the strain signal of actual gear pitting damage, the proposed method combines the finite element method and optimization method to obtain the friction coefficient at the different gear pitting level. Furthermore, by using calculated friction coefficient to obtain dynamic responses of different gear pitting states, the effects in dynamic responses of different types of friction coefficient are compared and analyzed.

Dynamics Modeling and Experimental Investigation of Gear Mechanism with Coupled Small Clearances.

Internal gear mechanism is widely used in micro-nano satellites due to its compact structure and high precision transmission. However, the vibration coupling caused by the small clearance coupling is more obvious and cannot be ignored under low speed, light load and zero gravity conditions. Based on the geometric relationship between radial clearance and backlash, a coupled model between dynamic backlash and radial clearance of internal meshing gear is established. Based on the conformal contact theory, the radial collision force model of the gear shaft and shaft sleeve considering the small clearances is established. Additionally, a multi-clearance gear rotor system test device is built to measure the vibration acceleration of the internal gear rotor system by an acceleration sensor and transmitted to the industrial computer through a signal collector for data processing. Through the comparison of simulation and experiment, the accuracy of the gear dynamics model is verified. The analysis results show that, compared with the traditional model, the calculation results of the gear mechanism model considering the small clearance coupling is closer to the experimental data.

Synthesis of landing dynamics on land-base high performance aircraft considering multi-variate landing conditions

Consideration of standard landing cases from technical guideline document is the traditional design practice followed to ascertain aircraft landing loads. A rationale approach on landing load generation and its impact on flexible airframe dynamic response is explored, considering multi-variate landing conditions for the first time on land-base high performance aircraft. Methodology on nonlinear landing dynamic response simulation is developed by amalgamating inputs such as nonlinear nose and main landing gear dynamic models, aircraft rigid body dynamics, low speed aerodynamic and thrust forces. True representation of landing gear nonlinear oleo-pneumatic strut and tire characteristics, variable geometric strut structural stiffness and nonlinear spin-up friction resulted in satisfactory correlation of vertical and longitudinal dynamic response simulation with experimental drop test results. The adequacy of lateral dynamic model is established from the compatibility condition of landing gear and tire dynamics. A down selection methodology is worked out considering total probability and first order sensitive multi-variate landing parameters such as pitch, roll and vertical descent speed, taking into account the plausible statistical variation. Transient dynamic response simulation is then performed for the critical landing cases, on a flexible airframe finite element model by inputting landing load time history as base excitation motion. The dynamic amplification of acceleration response on flexible fuselage nose location from the simulation, is verified with flight data accelerometer frequency response. The application of flexible dynamic responses in ensuring the structural integrity of airframe is elaborated. The proposed methodology on landing load generation is pragmatic, in comparison with the traditional design practice and provides insight during early design phase thereby achieving landing gear subsystem development in-unison with airframe structural clearance aspects.

Bearing internal load analysis and fatigue life estimation based on nonlinear dynamic model of a gear system

The bearing internal load distribution and fatigue life estimation are accomplished based on the bearing static model at present, ignoring the gear engagement. Besides, bearings are modeled as a linear spring in gear dynamic models, failing to analyze bearing internal load. This article aims to study the bearing internal load fluctuation and corresponding bearing life in gear systems. A nonlinear dynamic model of the gear-bearing system is built, considering the time-varying mesh stiffness, the static transmission error, backlash, bearing clearance, and the nonlinear bearing force. The dynamic model is capable of calculating the bearing internal load. Based on the internal load, fatigue life is acquired using the linear damage theory. The numerical results show that the gear engagement has a significant influence on the bearing internal load analysis, in which periodic fluctuation is related to the mesh frequency and shaft frequency, resulting in the bearing life affected by gear meshing. Compared with the fatigue life predicted under the bearing static model, evident deviations are observed, pointing to the significant role of the gear engagement in the analysis of fatigue life estimation.